8.2 Weak lensing by galaxies

A gravitational lens not only produces multiple images close to caustics, but also weakly distorted
images (arclets) of other background sources. The weak and noisy signals from several individual arclets
(not necessarily detected by eye, but rather numerically exploited with the help of image analysis) can be
averaged by statistical techniques to get the shear components and in Eq. 114 from the mean
ellipticity of the images. One can then get the convergence from the azimuthal average of
the tangential component of the shear. This is what is known as weak lensing. In the case of
galaxy-galaxy weak lensing, since the gravitational distortions induced by an individual lens are too
small to be detected, one has to resort to the study of the ensemble averaged signal around
a large number of lenses. This has been investigated in the context of MOND for a sample
of relatively-isolated galaxy-lenses, stacked by luminosity ranges [456]. The derived MOND
masses were obtained by fitting a point mass model to the lensing data within a distance of
200 kpc from the lens. While the MOND masses are perfectly compatible with the baryonic
masses in all galaxies less luminous than , it was found that the required MOND
mass-to-light ratios tended to be slightly too high () for the most massive and
luminous galaxies (). However, this whole result is dictated by only one data
point, which “pulls up” the result and make all the data points lie below the “best fit”, and the
curve is “pulled up” strongly by only the first point. Thus, the mass-to-light ratios could easily
be scaled down by a factor of two, making these galaxies in perfect agreement with MOND.
But it is also worth noting that due to the very large distances probed, the presence of some
weakly-clustering residual mass (hot dark matter, or some sort of “dark field” in the relativistic
MOND theories) could start playing a role at these distances. While ordinary neutrinos are still
too weakly clustering, a slightly more massive fermion such as a 10 eV-scale sterile neutrino
could cluster on these scales, and, of course, the presence of baryonic dark matter in the form
of dense molecular gas clouds could also be present around these very massive objects (see
Section 6.6.4).

Also related to weak lensing, it is important to recall that the “phantom dark matter” of MOND
(Eq. 33) can sometimes become negative in cones perpendicular to the direction of the external
gravitational field in which a system is embedded: with accurate enough weak-lensing data, detecting these
pockets of negative phantom densities around a sample of non-isolated galaxies could, in principle, be a
smoking gun for MOND [490], but such an effect would be extremely sensitive to the detailed distribution
of the baryonic matter, and finding a sample of galaxies with similar gravitational environments would also
be extremely difficult.